Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void init() {}
const int N = (int)1e6 + 34;
const long long INF = (long long)1e9 + 34;
int n, m;
int a[555][555];
int c[555], r[555];
int main() {
  init();
  int mxr = -N, mnr = N, mxc = -N, mnc = N;
  cin >> n >> m;
  int sum = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> a[i][j];
      sum += a[i][j];
    }
  }
  if (n == 1) {
    for (int j = 0; j < m; j++) {
      c[j] = a[0][j];
    }
    r[0] = 0;
  }
  if (m == 1) {
    for (int i = 0; i < n; i++) {
      r[i] = a[i][0];
    }
    c[0] = 0;
  }
  if (max(n, m) > 1) {
    c[0] = 0;
    for (int i = 0; i < n; i++) r[i] = a[i][0];
    for (int j = 1; j < m; j++)
      for (int i = 0; i < n; i++) {
        c[j] = a[i][j] - r[i];
      }
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) {
      if (a[i][j] != r[i] + c[j]) {
        cout << "-1\n";
        return 0;
      }
    }
  for (int i = 0; i < n; i++) {
    mnr = min(mnr, r[i]);
    mxr = max(mxr, r[i]);
  }
  for (int j = 0; j < m; j++) {
    mxc = max(mxc, c[j]);
    mnc = min(mnc, c[j]);
  }
  if (mnr + mnc < 0) {
    cout << "-1\n";
    return 0;
  }
  int dr = 0;
  int dc = 0;
  if (mnr < 0) {
    dc = mnr;
    dr = -dc;
  } else if (mnc < 0) {
    dr = mnc;
    dc = -dr;
  }
  while (n > m && mnr + dr > 0) {
    dr--;
    dc++;
  }
  while (n < m && mnc + dc > 0) {
    dr++;
    dc--;
  }
  int num = 0;
  for (int i = 0; i < n; i++) num += r[i] + dr;
  for (int j = 0; j < m; j++) num += c[j] + dc;
  cout << num << "\n";
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < r[i] + dr; j++) cout << "row " << i + 1 << "\n";
  }
  for (int j = 0; j < m; j++) {
    for (int i = 0; i < c[j] + dc; i++) cout << "col " << j + 1 << "\n";
  }
  return 0;
}